The first procedure you'll need to do 'on the morning of arrival into Southampton' will be to collect NEW replacement stateroom keys ( even if you are still occupying your original stateroom)
If you decide to disembark in Southampton to explore you will Swipe OUT at the gangway with the old card, and swipe IN on your return with your new key card. You will be able to embark back on the ship only when the embarkation procedures are underway ( You by-pass the check-in desks and show your key card to the terminal agent - you mention you are In -Transit.
Re your concerns about seasickness , Queen Mary 2 is poles apart from a cruise ship Silversea, you are sailing on a Transatlantic Ocean Liner, built for the itinerary you have chosen .